Question

Suppose that the height (in centimeters) of a candle is a linear function of the amount of time (in hours) it has been burning. After 6 hours of burning, a candle has a height of 19 centimeters. After 17 hours of burning, its height is 13.5 centimeters. What is the height of the candle after 15 hours?

Answer 1

14.5 cm

Explanation:

x is the time, y is the height

first find slope (m) using the points (6,19) and (17, 13.5):

m = (13.5-19) / (17-6) = -5.5/11 = -5.5/11 = -0.5 this means the height of the candle lowers by 0.5 cm every hour

pick either point and use point-slope form to find the y-intercept (b):

y - 19 = -0.50(x - 6)

y - 19 = -0.50x + 3

y = -0.5x + 22

for x = 15 hours, f(x) = -0.5(15) + 22 = 14.5 cm